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Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

Numerical Analysis · Mathematics 2024-06-26 Andrea Ebner , Matthias Schwab , Markus Haltmeier

Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even…

Numerical Analysis · Mathematics 2025-01-03 Tobias Long , Robert Barnett , Richard Jefferson-Loveday , Giovanni Stabile , Matteo Icardi

Person re-identification (re-id) aims to retrieve images of same identities across different camera views. Resolution mismatch occurs due to varying distances between person of interest and cameras, this significantly degrades the…

Computer Vision and Pattern Recognition · Computer Science 2021-09-17 Asad Munir , Chengjin Lyu , Bart Goossens , Wilfried Philips , Christian Micheloni

We present a new method for face recognition from digital images acquired under varying illumination conditions. The method is based on mathematical modeling of local gradient distributions using the Radon Cumulative Distribution Transform…

Computer Vision and Pattern Recognition · Computer Science 2022-02-23 Yan Zhuang , Shiying Li , Mohammad Shifat-E-Rabbi , Xuwang Yin , Abu Hasnat Mohammad Rubaiyat , Gustavo K. Rohde

We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is…

Numerical Analysis · Mathematics 2011-09-05 Jürgen Frikel

English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Ali Mohammad-Djafari

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…

Mathematical Physics · Physics 2015-06-17 Paolo Facchi , Marilena Ligabò , Sergio Solimini

In this paper we broadly consider techniques which utilize projections on rays for data collection, with particular emphasis on optical techniques. We formulate a variety of imaging techniques as either special cases or extensions of…

Computer Vision and Pattern Recognition · Computer Science 2014-02-12 Keith Dillon , Yeshaiahu Fainman

The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…

Numerical Analysis · Mathematics 2024-11-26 Matthias Beckmann , Robert Beinert , Jonas Bresch

In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…

Functional Analysis · Mathematics 2014-03-04 Swanhild Bernstein , Isaac Z. Pesenson

Radon transform and its inverse operation are important techniques in medical imaging tasks. Recently, there has been renewed interest in Radon transform for applications such as content-based medical image retrieval. However, all studies…

Computer Vision and Pattern Recognition · Computer Science 2017-10-12 Morteza Babaie , H. R. Tizhoosh , Amin Khatami , M. E. Shiri

Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…

Geophysics · Physics 2007-05-23 G. Vignoli , L. Zanzi

We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…

Optimization and Control · Mathematics 2019-11-18 Melanie Melching , Otmar Scherzer

Row-action methods play an important role in tomographic image reconstruction. Many such methods can be viewed as incremental gradient methods for minimizing a sum of a large number of convex functions, and despite their relatively poor…

Optimization and Control · Mathematics 2013-11-05 Martin S. Andersen , Per Christian Hansen

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…

Functional Analysis · Mathematics 2011-08-30 Isaac Pesenson , Eric Grinberg

We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling…

Numerical Analysis · Computer Science 2018-03-29 Shahar Tsiper , Yonina C. Eldar

Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…

Numerical Analysis · Mathematics 2015-02-19 Simon Maretzke

The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the…

Numerical Analysis · Mathematics 2007-05-23 Gaik Ambartsoumian , Sarah K. Patch

Many imaging technologies rely on tomographic reconstruction, which requires solving a multidimensional inverse problem given a finite number of projections. Backprojection is a popular class of algorithm for tomographic reconstruction,…

Image and Video Processing · Electrical Eng. & Systems 2020-06-03 Xueqing Liu , Paul Sajda

The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Lili Ma , YangQuan Chen , Kevin L. Moore